Advertisements
Advertisements
Question
Find the number of ways for 15 people to sit around the table so that no two arrangements have the same neighbours.
Advertisements
Solution
15 people can sit around a table in (15 – 1)! = 14! ways.
Total number of arrangements = 14!
Now, the number of arrangements in which any person can have the same neighbours on either side by clockwise or anticlockwise arrangements = `(14!)/(2!)`
∴ The number of arrangements in which no two arrangements have the same neighbours
= `14! - (14!)/(2!)`
= `14!(1 - 1/2)`
= `14! xx 1/2`
= `(14!)/(2!)`.
APPEARS IN
RELATED QUESTIONS
A party has 20 participants and a host. Find the number of distinct ways for the host to sit with them around a circular table. How many of these ways have two specified persons on either side of the host?
A committee of 20 members sits around a table. Find the number of arrangements that have the president and the vice president together.
Find the number of sitting arrangements for 3 men and 3 women to sit around a table so that exactly two women are together.
In how many different ways can 8 friends sit around a table?
Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangments where two specified delegates are always together
Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangments where two specified delegates are never together
Find the number of ways for 15 people to sit around the table so that no two arrangements have the same neighbours
Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated between two men
Find the number of seating arrangements for 3 men and 3 women to sit around a table so that exactly two women are together.
Fifteen persons sit around a table. Find the number of arrangements that have two specified persons not sitting side by side.
Answer the following:
There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many lines are there in total.
Answer the following:
There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many lines pass through D.
A group of 5 men and 4 women are arranged at random, one after the other. The probability that women and men occupy alternate seats is ______
The number of ways in which 51 books can be distributed among three students, each receiving 17 books, is ______
